1. CS 326A: Motion Planning ai.stanford.edu/~latombe/cs326/2007/index.htm Collision Detection and Distance Computation

2. Two Main Approaches  Hierarchical bounding volume hierarchies (pre-computation)  Feature tracking (pairs of closest features)

3.  Enclose objects into bounding volumes (spheres or boxes)  Check the bounding volumes first Bounding Volume Hierarchy Method

4.  Enclose objects into bounding volumes (spheres or boxes)  Check the bounding volumes first  Decompose an object into two Bounding Volume Hierarchy Method

5. BVH in 3D

6. Collision Detection Methods  Bounding Volume Hierarchy (BVH) methods: Good for few moving objects with complex geometry  Feature-Tracking methods: Good for few objects with moderate geometric complexity

7. Probabilistic Roadmaps Few moving objects, but complex geometry

8. Static vs. Dynamic Collision Checking C-space

9. Combining Bounding Volume and Feature Tracking Methods  S.A. Ehmann and M.C. Lin. Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition. Proc. 2001 Eurographics, Vol. 20, No. 3, pp. 500-510, 2001.  Use BVH to quickly identify close pairs of polyhedra  Use feature-tracking to check these pairs

10. Combining Bounding Volume and Feature Tracking Methods  T.Y. Li and J.S. Chen. 1998. Incremental 3D Collision Detection with Hierarchical Data Structures,Proc. ACM Symp. on Virtual Reality Software and Technology, p.139-144, Taipei, Taiwan

11. Collision Detection Methods  Bounding Volume Hierarchy (BVH) methods: good for few moving objects with complex geometry  Feature-Tracking methods: Good for few objects with moderate geometric complexity  Grid method: Good for many simple moving objects of about the same size (e.g., many moving discs/balls with similar radii)

12. Crowd Simulation Many moving objects, but simple geometry (discs) Need to also compute distances (vision, sounds)

13. Grid Method d  Subdivide space into a regular grid cubic of square bins  Index each object in a bin

14. Grid Method d Running time is proportional to number of moving objects